This book is dedicated to Lev Okun, who passed away in November 2015. He was a true pioneer in probing fundamental dynamics. The book has two objectives. First is to showcase Okun's impact for decades since 1963, when he published his remarkable book Weak Interaction of Elementary Particles. Second is to present the current progress of our scientific community in the studies of our Universe. New directions and possible future developments are discussed, often using the past as a guide. The authors mostly focus on CP asymmetries in the transitions of hadrons and leptons, but they also discuss their rare decays, and talk about axions and supersymmetry, and possible connections with dark matter, extra dimensions, baryogenesis and multiverse. This book is suitable for readers who know quantum mechanics and quantum field theories in general.